In the circuit shown in the figure, the angular frequency $$\omega$$ (in rad/s), at which the Norton equivalent impedance as seen from terminals b-b' is purely resistive, is _______.

A series RC circuit is connected to a DC voltage source at time t = 0. The relation between the source voltage V_S, the resistance R, the capacitance C, and the current i(t) is given below: $$$V_{s\;}=\;Ri(t)+\frac1c\int_0^ti(u)du$$$ Which one of the following represents the current f(t)?

In the figure shown, the value of the current I (in Amperes) is __________.

Let $${H_1}(z) = {(1 - p{z^{ - 1}})^{ - 1}},{H_2}(z) = {(1 - q{z^{^{ - 1}}})^{ - 1}}$$ , H(z) =$${H_1}(z)$$ +r $${H_2}$$. The quantities p, q, r are real numbers. Consider , p=$${1 \over 2}$$, q=-$${1 \over 4}$$ $$\left| r \right|$$ <1. If the zero H(z) lies on the unit circle, the r = ____________________________.